IEEE浮点数尾数向偶舍入-四舍六入五成双
# -*- coding: utf-8 -*-
"""
Created on Thu Jun 9 17:20:29 2022
@author: luogantt
"""
import numpy as np
#将十进制小数转化为二进制
def dec2bin(x):
x -= int(x)
bins = []
while x:
x *= 2
bins.append(1 if x>=1. else 0)
x -= int(x)
return bins
print(dec2bin(.8125))
def expo(cc):
n=0
while (not cc[n]):
n=n+1
print(n)
return n+1
"""
>0.5 --1
<0.5 --0
==0.5 if up==0 --0
==0.5 if up==1 --1
"""
#决定舍入项是否要进一位
def roundings(cc,exp):
drop= np.array(cc[exp+23:exp+23+4])
weight=np.array([1/2,1/4,1/8,1/16])
ifdrop=np.sum(weight*drop)
if ifdrop>0.5:
return 1
elif ifdrop<0.5:
return 0
else:
if cc[exp+23]==0:
return 0
else:
return 1
# 将小数位转换成 float32
def float32(exp,cc):
fric=cc[exp:exp+23]
strfric=''.join([str(k) for k in fric])
intfric= int(strfric,2)
round1= roundings(cc,exp)
if round1:
intfric=intfric+1
intfric1=bin(intfric)
intfric2=intfric1[2:]
intfric3=[int(k) for k in intfric2]
sum=0
for k in range(len(intfric3)):
sum=sum+intfric3[k]*2**(-1*(k+exp+1))
sum=sum+(2)**(-(exp))
print(sum)
return sum
cc1=dec2bin(0.1)
exp1=expo(cc1)
sum1= float32(exp1,cc1)
print( '小数位',sum1)
cc2=dec2bin(0.2)
exp2=expo(cc2)
sum2= float32(exp2,cc2)
print(sum2)
#
print('0.1+0.2=',sum1+sum2)
[1, 1, 0, 1]
1
2
3
0.10000000149011612
小数位 0.10000000149011612
1
2
0.20000000298023224
0.20000000298023224
0.1+0.2= 0.30000000447034836
IEEE浮点数尾数向偶舍入-四舍六入五成双
